4422
J . Am. Chem. Soc. 1985, 107,4422-4430
Comparison of Semiempirical and ab Initio Transition States Stefan Schroder and Walter Thiel* Contribution from Theoretische Chemie, Bergische Universitat-Gesamthochschule 0 - 5 6 0 0 Wuppertal 1, West Germany. Received December 5, 1984
Wuppertal,
Abstract: MNDO and MNDOC calculations are reported for 24 reactions of simple organic molecules. The results are compared with those from state-of-the-art ab initio calculations. Satisfactory agreement is generally found for the geometries, frequencies, and zero-point vibrational energies of transition states. The ab initio activation energies are reproduced more closely by MNDOC than by MNDO. The comparisons clarify the accuracy which may be expected in semiempirical calculations of transition states and thereby allow a more detailed justification for applying MNDO and MNDOC to the study of chemical reactions.
1. Introduction There are several semiempirical methods'-5 which have been designed for calculating potential surfaces of large molecules, e.g., M N D 0 3 and its correlated version M N D O C 5 For stable molecules, the reliability of these methods has been established by systematic comparisons with experimental data so that mean absolute errors are available for many ground-state properties3-' For transition states, such systematic tests have not been feasible due to the lack of experimental data, e.g., for transition-state geometries. As a consequence, semiempirical predictions for transition states have sometimes been met with scepticism based on the feeling that they merely represent uncertain extrapolations on potential surfaces. In view of the widespread use of semiempirical methods for computing chemical reactions (see, e.g., ref 8-10 for an incomplete list of recent M N D O applications), it is clearly desirable to establish their reliability in this connection more securely. In the absence of sufficient experimental data, this can only be done by comparing the semiempirical results with those from elaborate ab initio calculations. Fortunately, during the last 5 years (Le., after the publication of M N D 0 3 and the development of MNDOC5), ab initio transition structures have become available which have been fully optimized by analytical gradient techniques. These structures and the corresponding energies from state-ofthe-art ab initio treatments are not exact, of course, but they are considered reliable enough to serve as reference data for our purposes. The present paper provides a systematic evaluation of MNDO and MNDOC calculations for transition states. Comparisons with (1) Pople, J. A,; Segal, G. A. J . Chem. Phys. 1966, 44, 3289. (2) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H. J . Am. Chem. SOC.1975, 97, 1285. (3) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899,4907. (4) Nanda, D. N.; Jug, K. Theor. Chim. Acta 1980, 57, 95. Jug, K.; Nanda, D. N . Theor. Chim. Acta 1980, 57, 107, 131. (5) Thiel, W . J . Am. Chem. SOC.1981, 103, 1413. (6) Dewar, M. J. S.; Rzepa, H. S. J . Am. Chem. SOC.1978, 100, 784. (7) Dewar, M. J. S.; Ford, G. P.; McKee, M. L.; Rzepa, H. S.;Thiel, W.; Yamaguchi, Y. J . Mol. Struct. 1978, 43, 135. (8) Ford, G. P.; Scribner, J. D. J . Am. Chem. Soc. 1983,105, 349. Storch, D. M.; Dymek, C. J., Jr.; Davis, L. P. J . Am. Chem. SOC.1983, 105, 1765.
Apeloig, Y.; Ciommer, B.; Frenking, G.; Karni, M.; Mandelbaum, A.; Schwarz, H.; Weisz, A. J . Am. Chem. SOC.1983, Z05, 2186. Apeloig, Y.; Karni, M.; Stang, P. J.; Fox, D. P. J . Am. Chem. SOC.1983, 105, 4781. Dewar, M. J. S.; Chantrapunong, L. J . Am. Chem. SOC.1983, 105, 7152, 7161. Rayez, J. C.; Rayez, M. T.; Duguay, B. J. Chem. Phys. 1983, 78,827. Engelke, R.; Hay, P. J.; Kleier, D. A.; Wadt, W. R. J . Chem. Phys. 1983, 79, 4367. Dormans, G. J. M.; Fransen, H. R.; Buck, H. M. J . Am. Chem. SOC. 1984, 106, 1213. Carrion, F.; Dewar, M. J. S. J . Am. Chem. SOC.1984, 106, 3531. Dewar, M. J. S.; Kuhn, D. R. J . Am. Chem. SOC.1984, 106, 5256. Engelke, R.; Hay, P. J.; Kleier, D. A,; Wadt, W. R. J . Am. Chem. SOC.1984, 106, 5439. Turner, A. G.; Davis, L. P. J . Am. Chem. SOC.1984, 106, 5447. Bock, H.; Roth, B.; Maier, G. Chem. Ber. 1984, 117, 172. Lebrilla, C. B.; Maier, W. F. Chem. Phys. Lett. 1984, 105, 183. Frenking, G.; Heinrich, N.; Koch, W.; Schwarz, H. Chem. Phys. Lett. 1984, 105, 490. Frenking, G.; Schmidt, J. Tetrahedron 1984, 40, 2123. (9) Shea, J. P.; Nelson, S. D.; Ford, G. P. J . Am. Chem. SOC.1983, 105, 5451. Pudzianowski, A. T.; Loew, G. H.; Mico, B. A,; Blanchflower, R. V.; Pohl, L. R. J . Am. Chem. SOC.1983,105,3434. Pudzianowski, A. T.; Loew, G. H. J . Phys. Chem. 1983.87, 1081. Pudzianowski, A. T.; Loew, G. H. Int. J . Quant. Chem. 1983, 23, 1257. (10) Barone, V.; Bianchi, N.; Lelj, F. Chem. Phys. Lett. 1983, 98, 463.
0002-78631851 1507-4422$01.50/0
Scheme I H,C=CH,
'
+
H&=C
HC-CH,
A 5
\
2
+
HC=CH
H2
Hp
4
3
Scheme I1 14
HZC=O
*
F
HC-OH
10
trans
11
lljr H2
- HC-OH
7
t CO 13
Scheme 111 HJC-OH
cis
12
-
J
HZ
t H,C=O 19
H2C
t OH,
+
H,
21
HC-OH 20
Scheme IV H,
trans
-
32
C= C=O
M
25
H&
+
CO
26
HC-CH-0
-
34 0
27 28
'PO
HC'
:3
C=CH-OH 30
-
HCEC-OH 31
29
ab initio reference calculations are carried out for a set of 24 reactions of small organic molecules, with regard to transition structures, activation energies, zero-point vibrational energies, and transition-state frequencies. 2. Ab Initio Reference Data The selection of ab initio reference data from published material is based on the following guidelines. 0 1985 American Chemical Society
J . Am. Chem. SOC.,Vol. 107. No. 15, 1985 4423
Semiempirical and ab Initio Transition States Scheme V
-
CH,=CH-CH, 40
CH,-CH=CH, 40
O=CH-OH
43
7 HO-CeO
42
O=CH-CH=O
42 cis
45 7 H&=O
44
+
CO
46
O=CH-CH=O 44
cis
7 H2 + 47
2CO
48
(a) Transition structures are required to be fully optimized by gradient techniques and characterized by force constant analysis. (b) Geometry optimizations at the restricted Hartree-Fock (RHF) level must involve a basis set of at least split-valence quality. To be as consistent as possible, we accept only the standard basis sets developed by the Pople group, e.g., 3-21G," 4-31G,I2 and 6-31G*.I3 (c) Geometry optimizations at the correlated level are not included since we wish to compare semiempirical and ab initio R H F transition structures. The correlation effects on such structures are often fairly small, anyway (see, e.g., ref 16). (d) For all RHF-optimized transition structures, high-level energy calculations must be available which make use of basis sets with polarization functions and a suitable correlation treatment. (e) The reference systems must consist of the elements H,C,N, and 0 since MNDOC, unlike MNDO, has only been parametrized for these elements. Following these guidelines, we have selected ab initio reference calculations which deal with the potential surfaces of ethylene,14,1s f ~ r m a l d e h y d e , ' ~methanol,15J6 '~ ketene,I8 propene,I9formic acid,I9 and cis-glyoxal.20 In addition to these reference calculations,'620 there are a number of other ab initio studies on these system^,^^-^^ some of which are discussed below (see section 4). Schemes I-V show the investigated reactions which are denoted by capital letters whereas the minima and transition states involved are identified by boldface numbers. The selected set of 24 reactions includes six [ 1,2]- and two [ 1,3]-sigmatropic hydrogen shifts, five other (11) Binkley, J. S.;Pople, J. A,; Hehre, W. J. J . Am. Chem. SOC.1980, 102. 939. (12) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (13) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 16, 217. (14) Raghavachari, K.; Frisch, M. J.; Pople, J. A,; Schleyer, P. v. R. Chem. Phys. Lett. 1982, 85, 145. (15) Whiteside, R. A.; Binkley, J. S.;Krishnan, R.; DeFrees, D. J.; Schlegel, H. B.; Pople, J. A. 'Carnegie-Mellon Quantum Chemistry Archive"; Carnegie-Mellon University: Pittsburgh, 1980. (16) Harding, L. B.; Schlegel, H. B.; Krishnan, R.; Pople, J. A. J . Phys. Chem. 1980, 84, 3394. (17) Frisch, M. J.; Binkley, J. S.; Schaefer, H. F., 111. J . Chem. Phys. 1984,
--.
81. 1RR2
(18) Bouma, W. J.; Nobes, R. H.; Radom, L.; Woodward, C. E. J . Org. Chem. 1982, 47, 1869. (19) Rodwell, W. R.; Bouma, W. J.; Radom, L. Inr. J. Quant. Chem. 1980, 7 7 in7 --, _"..
(20) Osamura, Y.; Schaefer, H. F., 111; Dupuis, M.; Lester, W. A,, Jr. J. Chem. Phys. 1981, 75, 5828. (21) Nobes, R. H.; Radom, L.; Rodwell, W. R. Chem. Phys. Lett. 1980, 74, 269. (22) Goddard, J. D.; Schaefer, H. F., 111. J. Chem. Phys. 1979, 70, 5117. (23) Gcddard, J. D.; Yamaguchi, Y.; Schaefer, H.F., 111.J. Chem. Phys. 1981. 75. 3459. (24) Adams, G. F.; Bent, G. D.; Bartlett, R. J.; Purvis, G. D. J. Chem. Phys. 1981, 75, 834. (25) Frisch, M. J.; Krishnan, R.; Pople, J. A. J. Phys. Chem. 1981, 85, 1467. (26) Dupuis, M.; Lester, W. A., Jr.; Lengsfield, B. H., 111. Liu, B. J. Chem. Phys. 1983, 79, 6167. (27) Tanaka, K.; Yoshimine, M. J . Am. Chem. SOC.1980, 102, 7655. (28) Bernardi, F.; Robb, M. A,; Schlegel, H. B.; Tanachini, G. J . Am. Chem. SOC.1984, 106, 1198. (29) For earlier ab initio studies, see citations in ref 14, 16-28
Figure 1. Definition of transition structures.
15
17
Q-0 38
13
Figure 2. Planar transition structures drawn to scale. The solid lines show the optimized a b initio R H F geometries (defined as in Figure 1) while the crosses mark the positions of the atoms in MNDOC.
intramolecular rearrangements, four 1,l and three 1,2 eliminations of H2, and four other dissociation reactions.
3. Semiempirical Calculations The MNDO and MNDOC calculations were carried out by using standard parameters3ss and program^.^^*^' All geometries were optimized at the SCF level by employing the Davidon-Fletcher-Powell algorithm3* for minima and gradient norm m i n i m i ~ a t i o nfor ~ ~transition ,~~ states. In most cases, the automatic optimization program was successful in locating transition structures when starting the search at the corresponding published ab initio structure; if not, suitable starting points were found by the usual reaction coordinate or grid search techniques. Energies were evaluated at the MNDO SCF level' and the correlated MNDOC BWEN levelS as rec~mmended.'~A force constant analysis was performed for all MNDO S C F stationary points.
4. Results The transition structures are defined in Figure 1 and Table I. Figure 2 allows a visual comparison between the MNDOC and ab initio R H F geometries of all planar transition states studied. Tables I1 and 111list relative energies for the species 1-39 obtained from MNDO and MNDOC heats of formation and from ab initio (30) Thiel, W. In "Quantum Chemistry Program Exchange Catalog"; Indiana University: Bloomington, 1982; Vol. 14, program 438. (31) Routines for the location of transition states and for force constant analysis are available, e.g., from MOPAC: Stewart, J. P. In =Quantum Chemistry Program Exchange Catalog"; Indiana University: Bloomington, 1983; Vol. 15, program 455. (32) Fletcher, R.; Powell, M. J. D. Comput. J . 1963, 6, 163. Davidon, W. C. Compur. J . 1968, 10, 406. (33) McIver, J. W., Jr.; Komornicki,A. J . Am. Chem. SOC.1972, 94, 2625. (34) Weiner, P. K. Ph.D. Thesis, University of Texas, Austin, 1975. (35) Thiel, W. J . Am. Chem. SOC.1981, 103, 1420
4424 J . Am. Chem. Soc., Vol. 107, No. 15, 1985 Table I. Comparison of SCF-Optimized Transition Structures' svstem mint g r o w variablebF
MNDO
MNDOC
a b initiodVe
1.378 1.320 1.402 1.072 1.099 1.100 130.7 121.5 124.2 101.8 88.1 -1 13.9
1.397 1.364 1.321 1.103 1.096 1.098 113.0 120.4 127.5 100.7 84.8 -109.1
1.378 1.325 1.266 1.088 1.08 1 1.086 108.9 119.9 126.1 100.7 76.5 -107.5
1.319 1.284 1.682 0.8 13 1,091 1.089 135.3 119.5 127.0
1.313 1.253 1.507 0.836 1.090 1.089 136.0 117.9 128.9
1.322 1.249 1.461 0.838 h 126.4 114.3 130.1
1.271 1.563 1.367 1.370 0.985 1.076 1.05 1 148.0 160.9
1.275 1.542 1.419 1.384 0.919 1.08 1 1.072 157.1 136.2
1.323 1.557 1.265 1.272 0.886 h h 147.2 115.5
C'-C2H4H5
1.28 1 1.090 1.285 1.007 1.048 132.4 165.5 121.4
1.264 1.096 1.265 1.040 1.054 134.4 178.6 120.5
1.308 h 1.374 0.829 h 139.3 118.5 h
C'C2 C1H3 C2H3 C1H4 H4CLC2
1.270 1.37 1 1.322 1.059 167.0
1.261 1.402 1.269 1.067 172.7
1.237 1.459 1.170 1.062 180.4
c102
1.283 1.303 1.247 1.098 121.4
1.260 1.280 1.278 1.112 119.5
1.270 1.219 1.175 1.095 115.9
1.180 1.142 1.531 1.060 157.2 113.4
1.168 1.147 1.433 1.080 159.3 111.3
1.134 1.094 1.739 1.328 164.5 114.7
1.328 0.942 1.127 120.8 110.6 91.5
1.314 0.929 1.137 119.5 108.5 91.3
1.347 0.951 1.109 115.2 104.9 90.1
1.255 1.470 1.293 1.058 92.7 77.2
1.240 1.412 1.292 1.039 96.0 73.8
1.231 1.482 1.169 1.112 97.0 72.1
1.313 1.451 1.406 0.995 1.114
1.299 1.447 1.394 0.984 1.115
1.310 1.385 1.408 0.947 1.087
C2H3 C2H4 C'H5 C1H6 H4C2C1 H5C'C2 H6C1C2 H4C2C1H3 H5C'C2H3 H6C'C2H3 6
c1c2
C2H3 C2H4 H3H4 C1H5 C'H6 H3C2C1 H*C'C2 H6C1C2
c1c2 C1H3 C2H3 C2H4 H3H4 C2H5 C'H6 H5C2C' H6C'C2 8
C'C2
C2H3 C2H4 H4H5 C'H6 H3C2C1 H6C1C2 9
14
C'H3 0 2 ~ 3
C'H4 ~ 4 ~ 1 0 2
15
C'02
C'H3 C'H4 H3H4 ~ 3 ~ 1 0 2 ~ 4 ~ 1 0 2
16
C'02 0 2 ~ 3
C'H4 ~ 3 0 2 ~ 1 ~ 4 ~ 1 0 2
H302C1H4 17
C'O2 0 2 ~ 3
C1H4 H3H4 ~ 3 0 2 ~ 1
~ 4 ~ 1 0 2
22
Schroder and Thiel
c103 0 2 ~ 3
C'H4 H3H4 C1H5
h
ref
Semiempirical and ab Initio Transition States
J . Am. Chem. SOC.,Vol. 107, No. 15, 1985 4425
Table I (Continued)
svstem 22
point group
c,
variableb" ~ 3 0 2 ~ 1 ~ 4 ~ 1 0 2 ~ 5 ~ 1 0 2
H5C'02H3 23
CI
C'O2 C1H3 0 2 ~ 3 0 2 ~ 4
C1H5 C'H6 ~ 4 0 2 ~ 3
H5C1H6 H5C1M H6C1M 24
(2'02 0 2 ~ 3
C1H4 C'H5 C'H6 H5H6 ~ 3 0 2 ~ 1
~ 4 ~ 1 0 2
H5C1H4 H6C1H4 H5C1H6 ~ 5 ~ 1 0 2
H6C'02 H302C'H4 33
CI
C'C2 c203
C'H4 C2H4 C1H5 cv03
H5C'C2 H4C2C'03 H5C'C203 34
CI
C'C2 cl03
c203
C'H4 C2H4 C1H5 H5C'C2 H4C1C203 H5C'C203 35
Cl
C1CZ cl03
c203
C2H4 C1H5 cv03
H4C2C1 H5C'C2 H4C2C'03 H5C1C203 36
CI
C'C2 c203
C2H4 0 3 ~ 4
C1H5 clc203
H5C1C2 H4C2C'03 H5C'C203 37
Cl
ClC2 cl03 c203
C'H4 0 3 ~ 4
C'H5 cv03
MNDO
MNDOC
ab initiodse
ref
63.7 103.2 119.3 108.7
62.3 104.8 120.1 107.8
51.5 105.3 119.8 106.0
1.897 1.196 1.196 0.941 1.09 1 1.091 98.1 114.0 108.5 108.5
1.816 1.222 1.216 0.930 1.100 1,100 93.0 108.5 107.5 107.5
1.806 1.308 1.116 0.951 1.077 1.080 107.0 110.8 108.3 108.3
1.327 0.951 1.097 1.660 1.289 0.859 112.0 113.9 95.4 112.1 30.7 108.6 119.7 162.1
1.325 0.938 1.111 1.533 1.262 0.882 109.8 110.4 90.4 111.5 35.1 106.7 120.5 166.4
1.347 0.947 1.084 1.574 1.298 0.852 108.6 109.1 83.4 106.6 32.7 101.4 113.8 162.9
j
1.306 1.213 1.592 1.249 1.049 156.0 173.2 180.0 180.0
1.401 1.188 1.597 1.237 1.101 156.1 112.4 151.8 118.4
1.342 1.197 1.634 1.194 1.078 154.2 122.0 166.5 1 13.6
n
1.424 1.391 1.446 1.454 1.354 1.082 166.9 113.8 -149.9
1.422 1.360 1.457 1.454 1.354 1.082 167.7 113.2 -155.2
1.349 1.376 1.783 1.327 1.385 1.063 146.1 108.7 -162.3
n
1.333 1.913 1.286 1.086 1.053 93.8 137.6 168.0 180.0 0.0
1.322 1.924 1.272 1.098 1.064 95.8 134.2 164.6 180.0 0.0
1.280 1.918 1.347 1.065 1.053 93.8 138.6 167.2 178.1 51.4
n
1.247 1.312 1.206 1.488 1.050 150.0 167.1 180.0 180.0
1.241 1.299 1.194 1.525 1.06 1 148.8 159.6 180.0 180.0
1.218 1.364 1.151 1.466 1.052 166.0 172.5 178.9 174.2
n
1.499 1.899 1.276 1.403 1.239 1.091 86.0
1.521 1.854 1.258 1.377 1.227 1.104 83.1
1.479 1.827 1.350 1.360 1.239 1.087 80.3
n
j
I
m m
4426 J. Am. Chem. SOC.,Vola107, No. 15, 1985
Schroder and Thiel
Table I (Continued) system
point group
variablebVc
37
c1
H4C1C2 H'C1C2 H4C'C203
HSC1C203 38
c,
C'C2 C'O'
cz03 C1H4 0 3 ~ 4
C2HS
cv03 H4C1C2 HSC2C' 39
CI
C'C* c203 0 3 ~ 4
C'H' C2H5 clc203 ~ 4 0 3 ~ 2
H5C'C2 H40'C2C1 H5C'C203 41
c 2
C'C2 C'H4 C2H4 C2H5 C'H6 C1H7 C'C2C' H6C'C2 H7C1C2 H6C'C2C'
H7C1C2C' 43
O'C2 0 1 ~ 4
C2H4 C2H5 0 ~ 0 3 45
C'C2 C20'
c104
CIHS C2HS C'H6 clc203 ~ 2 ~ 1 0 4 ~ 6 ~ 1 0 4
47
MNDO 82.4 119.1 6.3 -108.4
MNDOC 83.6 111.4 4.6 -105.8
ab initiod,' 87.7 110.9 13.7 -99.3
1.333 1.771 1.378 1.275 1.303 1.070 81.6 91.6 151.2
1.327 1.776 1.350 1.238 1.375 1.078 83.1 99.5 148.2
1.287 1.856 1.449 1.245 1.412 1.055 85.2 100.6 148.1
n
1.288 1.314 0.955 1.413 1.322 163.4 111.1 58.4 110.4 -160.5
1.282 1.311 0.942 1.431 1.277 164.8 109.3 55.8 112.3 -157.6
1.258 1.312 0.955 1.314 1.303 170.0 115.7 60.8 102.2 -164.0
n
1.424 1.457 1.859 1.078 1.094 1.100 101.2 121.4 120.9 -133.4 77.3
1.416 1.432 1.845 1.082 1.096 1.100 100.0 121.4 120.0 -137.5 77.6
1.401 1.532 1.839 1.076 1.079 1.076 108.9 122.4 116.9 -146.5 68.3
0
1.294 1.318 1.689 1.087 100.7
1.282 1.307 1.661 1.095 101.6
1.269 1.335 1.590 1.065 108.5
0
2.110 1.174 1.213 1.599 1.108 1.112 112.2 111.3 122.5
2.016 1.159 1.199 1.594 1.123 1.128 110.9 114.5 119.3
2.216 1.146 1.208 1.916 1.08 1 1.107 101.2 98.6 121.2
ref
n
P 7
4
1.684 1.703 2.068 P. r 1.180 1.163 1.144 1.470 1.410 1.548 0.884 0.922 1.097 clc203 135.6 140.2 149.6 H5C'C2 75.0 74.6 69.9 " A complete geometry definition is given for each system, unles noted otherwise. A few of the structures listed have more than one negative eigenvalue of the force constant matrix (e.g., 7, 45, 47; see text). bSee Figure 1 for geometry definition. 'Bond length A'W (in A), bond angle A'WC' (in deg), dihedral angle A'E'C'D' (in deg), and angle A'-B'C'D' (in deg) of A-B with plane BCD. d6-31G* basis for 5-24, 4-31G basis for 33-43, 3-21G basis for 45 and 47. CSomeof the values given have been computed from the literature data. The sign of some dihedral angles has been switched to conform with out sign convention. fReference 15. gReference 14. *Value not given in ref 14. 'Angle taken from Figure 1 of ref 14 (no unambiguous definition). jReference 16. 'SDMC4(DZP): C ' 0 2 1.183, C'H3 1.096, C'H4 1.637, H3H4 1.301, H3C102162.7, H 4 C 1 0 2110.2 (ref 26). 'The geometry of 23 is defined incompletely in ref 16. m M is the midpoint of 02-H3. "Reference 18. "Reference 19. PReference 20. qSTO-3G: C'C2 2.037, C I H S 1.662, C2C104108.7 (ref 20). 'STO-3G:C1C21.923, H5H60.981, C'C203 144.3 (ref 20).
C'C2
c203 C1H5 HSH6
total energies. The ab initio R H F results in Tables I1 and I11 refer to the basis set used in the geometry optimizations, i.e., RHF/6-31G* in Table I1 and RHF/4-31G in Table 111, while the correlated a b initio results, Le., MP4(SDQ) in Table I1 and MP3 in Table 111, refer to the 6-31G** basis set. Comparison between the last two columns in Table I1 for systems 1-16 indicates how much high-level correlated ab initio energies (MP4(SDQ)/6-31G**) may change by further theoretical refinements; these changes may be taken as an error estimate for
the best ab initio energies in Table I11 (MP3/6-31G**). Table IV lists the semiempirical and ab initio activation energies (barrier heights without zero-point corrections) for all reactions defined in Schemes I-V. The activation energies refer to the endothermic reactions so that any errors in the semiempirical results should mainly be associated with the transition states, the energies of the stable educts normally being given r e l i a b l ~ . ~Figure , ~ 3 shows the correlation between the semiempirical and ab initio activation energies for reactions A-T (see Table IV). Table V compares
J. Am. Chem. SOC.,Vol. 107, No. 15, 1985 4421
Semiempirical and ab Initio Transition States
Table IV. Activation Energies (kcal/mol)"
Table 11. Relative Energies (kcal/mol)" for 1-24 ab initio resultsc system
MNDO
C2H4
1 2 3 4 5 6 7 8 9
0.0 73.0 106.9 43.7 95.1 124.8 149.4 125.4 138.1
MNDOCb 0.0 58.9 86.2 40.7 78.7 100.4 140.3 115.9 105.2
CH2O
10 11 12 13 14 15 16 17
0.0 46.5 46.4 27.5 108.7 96.5 66.9 155.9
0.0 33.6 32.1 5.9 93.3 71.3 56.5 125.5
a b initio
RHF" MP4(SDQ)e BEST/ 0.0 0.0 0.0 77.9 68.6 78.1 93.38 88.8 94.6 47.4 53.0 54.6 77.7 82.1 80.7 99.7 115.6 104.9 133.2 151.8 140.9 1 15.9 122.6 129.7 95.59 105.2 101.5
0.0 52.0 57.7 1.o 104.7 108.5 80.4 132.1
0.0 54.3 59.6 2.8 91.0 95.5 85.5
0.0 53.2 58.5h 3.2 84.7 85.9' 84.4* j
i
0.0 0.0 0.0 0.0 26.5 26.9 26.1 20.3 81.0 53.9 78.5 81.3 95.6 103.9 103.9 85.3 102.5 128.6 115.5 103.0 1 m 91.1 101.7k 95.9 96.1 82.7 102.2k Not including any corrections for zero-point vibrational energies. b M N D O C BWEN at MNDOC S C F geometries. 'References 14, 36, and 37 for 1-9; ref 15-17 for 10-24. "RHF/6-31G* at RHF/6-31G* geometries, except for 23-24.k e MP4(SDQ)/6-31G** at RHF/63 1G* geometries. /Unless noted otherwise: for C2H4, MP4(SDQ)/631G** at RHF/6-31G* geometries with triple-substitution correlation corrections and triple-basis split corrections; for C H 2 0 , MP4(SDTQ)/6-3 1 l++G(3df,3pd) at MP2/6-3 lG* geometries; for CH3OH, MP4(SDQ)/6-31G** at MP2/6-31G* geometries. gMP4(SDTQ)/6-311G** at MP2/6-31G* geometries, energies relative to 4. *Derived from column MP4(SDQ), energies relative to 11. 'Reference 26 gives 86.0 f 2.5 kcal/mol. 'No correlated value available. kRHF/6-31G** at RHF/6-31G* geometries, energy for 23 (24) relative to 21 (20). 'The MP4(SDQ) energy of 23 lies below that of 21. transition structure was found at the MP2/6-31G* level. CH,OH
0.0 25.1 71.6 103.9 135.3 109.4 101.2
18 19 20 21 22 23 24
Table 111. Relative Energies (kcal/mol)" for 25-39 ab initio results' system
MNDO
MNDOCb
RHF"
MP3'
0.0 0.0 0.0 0.0 108.2 76.4 83.0 90.1 70.6 64.5 76.8 84.2 65.5 55.3 78.9 58.8 62.4 75.8 88.5 80.3 86.4 72.3 75.2 83.7 19.0 21.9 31.8 36.0 108.5 76.9 81.2 83.2 80.5 74.2 141.2 119.2 145.1 121.3 83.1 84.8 94.7 89.3 124.6 105.7 126.3 113.7 164.4 126.5 160.1 138.5 148.1 123.8 141.0 118.6 107.7 78.5 92.2 80.2 " Not including any corrections for zero-point vibrational energies. 'MNDOC BWEN at MNDOC S C F geometries. 'Reference 18. dRHF/4-31G at RHF/4-31G geometries. .MP3/6-31G** at RHF/ 4-31G geometries.
CZH2O
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
the zero-point vibrational energies at the MNDO and ab initio R H F level which are based on the harmonic vibrational frequencies obtained from force constant analysis. These frequencies are listed in Table VI for the species 10-17 on the CHzO potential surface. In the remainder of this section, we shall present the results for the reactions in Schemes I-V. The discussion in the next section will then provide a general evaluation.
reaction
MNDO
MNDOC RHF BEST 77.96 78.7 82.1 A 95.1 115.6 99.7 B 124.8 100.4 133.2 C 149.4 140.3 151.8 68.5 D 81.7 75.2 75.1 48.1 94.4 64.5 50.6 E 84.7 104.7 F 108.7 93.3 85.9 G 96.5 71.3 108.5 31.2 20.4 22.9 28.4 H C 131.1 I 128.4 119.6 102.5 115.5 J 135.3 128.6 98.3" 103.9' 109.4 91.1 K 101.5d 96.1 82.7 L 101.2 90.1 108.5 83.0' M 76.9 81.2 80.5 u 84.2' 83.2 66.2 62.5 0 75.7 63.9 P 9.0 6.2 5.6 18.7 48.0 52.5 38.3 85.7 Q 94.5 77.7 R 83.8 105.6 S 104.6 128.3 102.5 145.4 T 56.6 60.4 47.76 88.7 92.9' 107.6e U 88.5 95.1 V 44.3' 66.6 59.5' 68.5 W C 73.7 100.49 95.9 76.09 X 6 1.6* 65.5 104.4 "Based on the data in Tables I1 and 111, unless noted otherwise. Entries in column BEST are obtained from column BEST in Table I1 and column MP3 in Table 111. bEndothermicity of reaction, no barrier. CNocorrelated value available. "RHF/6-3lG** at RHF/6-31G* geometries (ref 16). .RHF/4-31G at RHF/4-31G geometries (ref 19). /CEPA/DZP at RHF/4-31G geometries (ref 19). gRHF/3-21G at RHF/3-21G geometries (ref 20). *SDCI/3-21G with Davidson correction at RHF/3-21G geometries (ref 20).
Table V. Zero-Point Vibrational Energies (kcal/mol) svstem
MNDO ab initio SCF" system
MNDO
ab initio SCF"
1 2 3 4 5 6 7
33.5 34.4 25 21.6 21.8 31.0 26 14.7 14.8 31.6 27 19.9 19.2 22.9 23.0 25.0 28 21.9 21.4 25.1 30.9 29.7 29 21.7 20.5 26.1 30 21.2 20.8 28.1 25.5 26.7 31 22.1 22.2 8 26.7 32 16.0 C 27.8 9 20.4 33 18.0 17.9 21.7' 10 18.0 34 18.2 17.0 18.3 11 17.8 35 20.0 19.0 18.2 12 17.5 36 17.7 16.9 17.8 13 9.5 37 16.9 16.3 10.1 14 13.9 13.9 38 18.6 17.6 15 12.6 12.2 39 18.5 17.4 16 15.6 40 52.3 C 15.4 17 10.8 C 41 49.1 c 18 33.9 34.7 42 22.7 C 19 24.1 24.9 43 19.8 C 20 23.9 24.8 44 25.3 C 25.7 21 25.7 45 21.1 21.1 28.7 22 26.8 46 21.4 C 23 29.2 47 16.3 17.1 29.6 24 27.6 28.8 48 13.0 C "6-31G* basis for 1-24, 4-31G basis for 30, and 3-21G basis for 25-29 and 31-47 (see ref 14, 16, 18). bThe value for 9 is 1.3 kcal/mol below that for 3 (ref 36). CNotavailable.
Scheme I. The C2H4Surface. The general features of the potential surface are analogous in MNDO, MNDOC, and RHF/6-3 1G*. All three methods predict four genuine transition states (5, 6, 8, and 9 ) and one stationary point (7) with two negative eigenvalues of the force constant matrix. The optimized MNDOC and RHF/6-3 l G * geometries for 5-9 are generally quite similar (see Figures 1 and 2 and Table I) except for the H6C'C2 angle in 8. The MNDO geometries sometimes deviate more strongly, e.g., with regard to the angles in 5, 7 , and 8 , but
4428 J. Am. Chem. SOC.,Vol. 107, No. 15, 1985
Schroder and Thiel
Table VI. Vibrational Frequencies (cm-I)’
system 1V
symmetry a1 bl b2
11
a’
12
a” a’
a” 13d
0s U
MNDO
ab initiob
3302 2115 1490 1186 3255 1210 3935 3200 1702 1494 1146 963 3792 3159 1713 1385 1165 1014 4294 2383
3161 2030 1680 1336 3233 1383 4045 3101 1647 1446 1333 1128 3985 2992 1611 1450 1370 1041 4643 2439
system 14
symmetry a’
15e
a” a’
16
a” a
17
a’
MNDO
ab initiob
3284 2772 1839 1246 30461’ 500 2933 2236 1824 892 25391‘ 944 401 1 3063 1612 1313 921 1316i 2337 1859 1764 711 50791‘ 773
3168 2816 1649 1431 2710i 649 3263 2149 1306 755 21841’ 1056 4070 2977 1524 1281 890 13641‘
f
a’’ OThe transition states 14-17 have one imaginary frequency. bRHF/6-31G* values from ref 16. For other ab initio values see ref 17, 23, 24, and 26. CHarmonizedexperimental frequencies: a, 2978, 1778, 1529; b, 1191; b2 2997, 1299 (ref 45). refers to H2 (CO). eMCIO(DZP): a’ 3207, 1815, 1282, 791, 1853i; a” 849 (ref 26). ‘fNot available.
1501
0
C -.7,
I
c-
HJ
”
,,-y p7
P
‘ L . . . -
c2 H4 CH,O CH, OH c2 H2O Figure 3. Correlations between calculated activation energies, as given numerically in Table IV. From left to right, the activation energies are always drawn in the order: MNDO-ab initio RHF-ab initio BEST-
MNDOC. still resemble the RHF/6-3 lG* structures qualitatively. The best correlated ab initio energies are reproduced much better by MNDOC than by M N D O (see Table 11). The MNDOC activation energies are in the same sequence as the ab initio ones, with fairly small quantitative discrepancies (see Figure 3). The major shortcoming of the semiempirical predictions concerns the intermediates 2 and 3. In the best correlated ab initio treatments, there is no potential well for ethylidene 214 and a very shallow whereas MNDO and MNDOC (like ab one for vinylidene 3,36937 initio RHF14,36-38) predict them to be stable minima, with ap1 and 3 4. preciable barriers for the rearrangements 2 MNDO, MNDOC, and the ab initio R H F treatment thus substantially overestimate the barriers for these [ 1,2]-hydrogen shifts. With regard to the conversion of ethylene to acetylene, Scheme I offers three mechanistic alternatives. The direct 1,2 elimination of hydrogen is ruled out by all computational methods. The two-step pathway via 5 and 8 is favored by M N D O (incorrectly),
-
-
(36) Krishnan, R.;Frisch, M. J.; Pople, J. A.; Schleyer, P. v. R. Chem. Phys. Lerr. 1981, 79, 408. (37) Pople, J. A. Pure Appl. Chem. 1983, 55, 343. (38) Schaefer, H. F., 111 Acc. Chem. Res. 1979, 22, 289.
while MNDOC and the ab initio treatments predict a two-step mechanism via vinylidene, Le., a 1,l elimination of hydrogen via 6 followed by a [ 1,2]-hydrogen shift via 9. Scheme 11. The CH20 Surface. All methods studied produce four genuine transition states (14-17) with remarkably similar geometries (see Figures 1 and 2 and Table I). The lowest activation energy is always associated with the internal rotation (H) in hydroxycarbene via 16 and the highest one with the 1,2 addition (I) of H2 and CO via 17 (see Figure 3 and Table IV). The best correlated ab initio calculation^^^ predict the activation energies for the [1,2]-hydrogen shift (F) and the 1,l elimination (G) in formaldehyde to be almost equal, whereas MNDO and MNDOC give a higher activation energy for F which is partly due to their tendency to overestimate the barriers to [ 1,2]-hydrogen shifts (see above). Table VI compares harmonic vibrational frequencies at the MNDO and RHF/6-3 lG* level. Deviations between calculated frequencies are of the order of 10% for the transition states 14-16 and slightly smaller (typically 7%) for the minima 10-13. Since these deviations occur in both directions, the calculated zero-point vibrational energies for 10-16 show excellent agreement (see Table V), with mean absolute deviations of 2% (0.4 kcal/mol) between MNDO and RHF/6-31G* results. This type of agreement is also found for other systems (see Table V). The 1,l elimination (G) of hydrogen from formaldehyde has recently been studied by extensive ab initio MCSCF-CI calculations.26 The final barrier height of 86.0 f 2.5 kcal/mol agrees with the best ab initio value” of 85.9 kcal/mol included in Tables I1 and IV. With regard to transition-state geometries and frequencies, however, the new resultsz6often differ appreciably from previous ones16s23 (see best new data for 15 in footnote k of Table I and footnote e of Table VI). These differences provide a rough measure of the uncertainties which may be expected for all ab initio reference data in Tables I and VI. Scheme 111. The CH30H Surface. Three unimolecular decompositions of methanol are studied. For the 1,2 elimination (J) and the 1,l elimination (L) of hydrogen, all methods predict genuine transition states (22 and 24) with similar geometries (see Figure 1 and Table I). The 1,l elimination is always favored, being the lowest of all three decomposition pathways according to MNDO, MNDOC, and the best correlated ab initio treatment (see Figure 3 and Table IV). The third decomposition (K) of methanol leads to the formation of singlet methylene and water, the reverse reaction being a
Semiempirical and ab Initio Transition States carbene insertion. The published16 RHF/6-3 l G * transition structure 23 for this reaction resembles optimized M N D O and MNDOC structures (see Table I) with two negative eigenvalues of the force constant matrix. The genuine MNDO and MNDOC transition states (energies see Table 11) represent only a weak interaction between singlet methylene and water (compare, e.g., the optimized MNDO (MNDOC) values C ' 0 2 2.152 (2.124) A and C1H32.425 (2.388) A with the values in Table I). Hence, the semiempirical and the ab initio S C F transition structures for this carbene insertion are qualitatively different. The MNDO and MNDOC barriers for the insertion are fortuitously close to the RHF/6-31G* value (5.5 and 5.8 vs. 6.1 kcal/mol; see 21 and 23 in Table 11); however, at the best correlated ab initio level, the barrier disappears completely,I6 so that the semiempirical results for this reaction must be regarded as misleading. Scheme IV. The C2H20Surface. The potential surface of ketene is the most complicated one presently studied since the ab initio reference calculation^'^ involve seven minima (25-31) and seven transition states (33-39). All these minima and transition states are also found in MNDO and MNDOC calculations. For the conversion 26 25, there is apparently no barrier at the ab initio level,l* whereas M N D O and MNDOC give a very small barrier (0.3 and 0.5 kcal/mol, respectively); the corresponding C, transition state 32 is characterized in MNDO (MNDOC) by the data CC 2.753 (2.783) A, OCC 169.1' (167.9'), and C-CHI 89.2' (91.1'). The calculated MNDO, MNDOC, and RHF/4-3 1G18transition structures 33-39 are generally in satisfactory qualitative agreement, but some more specific comments seem appropriate (see Figure 1 and Table I). For 33, the MNDOC and ab initio geometries are fairly similar, whereas MNDO deviates appreciably with regard to the position of the (nonreactive) atom H* bonded to the carbenoid center C ' (see angles involving H5). For 34, MNDO and MNDOC underestimate the length of the breaking C 2 0 3bond. For 35, the MNDO and the MNDOC transition structures are planar in contrast to the ab initio one; however, this discrepancy is not too serious because the potential surface is quite flat with respect to nonplanar deformations; in fact, optimizations starting from the RHF/4-3 1G structure of 35 converge to nonplanar MNDO and MNDOC structures under the default criteria of our program and produce the planar structures only when using more stringent convergence criteria. For 36, analogous remarks apply as for 35; here, however, the deviations from planarity in the ab initio structure are extremely small, anyway. For 37-39, MNDO, MNDOC, and RHF/4-3 1G* predict transition structures of remarkable similarity (see also Figure 2). This is particularly gratifying for structures 37 and 38 which correspond to rather complicated rearrangements, i.e., concomitant ring openings and hydrogen shifts. With regard to relative energies (Table 111) and activation energies (Figure 3 and Table IV), the best ab initio results (MP3/6-31G**) are reproduced more closely by MNDOC than by MNDO. All methods predict ketene 25 to be the most stable isomer on the surface followed by hydroxyacetylene 31, but only MNDOC and MP3/6-31G** put oxiranylidene 28 in third place, significantly below the other isomers. Both MNDOC and the ab initio treatments predict the same sequence of activation energies (except for reactions M, and N, R, see Figure 3), the quantitative discrepancies between the MNDOC and MP3/631G** values being normally fairly small; as usual, however, MNDOC tends to overestimate the barriers to [ 1,2]-hydrogen shifts (see reactions R and T in Figure 3). The semiempirical calculations arrive at a number of qualitative conclusions which are the same as in the previous ab initio study:'* Hydroxyacetylene 31 is predicted to be a potentially observable isomer, the rate of its conversion to ketene 25 being determined by the barrier to the initial [1,2]-hydrogen shift via 36 (see reaction R in Figure 3). Oxiranylidene 28 is also expected to be observable since there seems to be no path to ketene with a very low activation energy. On the other hand, oxirene 29 is found to rearrange easily to ketene, the rate-determining step being the ring opening via 35 (see reaction P in Figure 3).
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J . Am. Chem. SOC., Vol. 107, No. 15, 1985 4429
The major discrepancy in the qualitative conclusions concerns formyl-methylene 27 and hydroxyvinylidene 30. These isomers turn out to be unstable at the best correlated ab initio level since the barriers for the rearrangements via 33 and 39 vanish. MNDO and MNDOC as well as the ab initio RHF/4-31G approach incorrectly predict potential wells for 27 and 30 (analogous to the case of ethylidene 2; see above). Scheme V. Other Reactions. The transition structures 41 and 43 for the [1,3]-hydrogen shifts in propene and formic acid belong to the point groups C, and C,,, respectively, the symmetry being derived from the fact that these antarafacial shifts are narcissistic reactions.39 The optimized geometries of 41 and 43 are quite similar at the MNDO, MNDOC, and RHF/4-31G19 levels (see Figures 1 and 2 and Table I). The semiempirical activation energies (see Table IV) are close to the best ab initio value in the case of propene (reaction U) but too high in the case of formic acid (reaction V). The last two reactions in Scheme V represent unusual unimolecular decompositions of cis-glyoxal leading to formzldehyde and carbonmonoxide (reaction W via 45) or to hydrogen and two carbonmonoxide molecules (reaction X via 47). Both in the ab initio reference calculationsZ0and in the present semiempirical study, the geometry optimizations for 45 and 47 were constrained to C, and CZLsymmetry, respectively. Therefore, the resulting structures usually do not correspond to genuine transition states, as can be seen from the number of negative eigenvalues of the force constant matrix for 45 (47): MNDO, MNDOC, and RHF/STO-3G 2 (3), RHF/3-21G 1 ( l ) , R H F / D Z and RHF/DZP (2).20 The qualitative features of the optimized stationary points 45 and 47 are the same in MNDO, MNDOC, and the ab initio R H F treatmentsZo(see Figures 1 and 2 and Table I for a comparison with RHF/3-21G20) although MNDO and MNDOC underestimate the length of the breaking CC bond. Quantitatively, the MNDO and MNDOC geometries for 45 and 47 are closest to those obtained from RHF/STO-3G (see footnotes q and r in Table I). With regard to activation energies (see Table IV), no correlated ab initio value is available for reaction W so that the MNDOC value is probably the most reliable one. For reaction X, MNDOC and the best correlated ab initio treatment yield similar estimates for the barrier. Since the optimized structures for 45 and 47 do not qualify as genuine transition states (see above), the "true" MNDO and MNDOC activation energies for reactions W and X are expected to be somewhat lower than listed in Table IV. Moreover, the zero-point correlations will reduce the effective semiempirical barriers further, by about 4 kcal/mol for W and 9 kcal/mol for X (see Table V) so that the effective MNDOC barriers should be slightly below 70 kcal/mol for W and 57 kcal/mol for X. These MNDOC predictions are compatible with recent experimental e ~ i d e n c e : ~ A ~ ~photo~' chemical molecular beam study finds both dissociation channels W and X to be open at an excitation energy of 65 kcal/m01,~~ and a thermal shock-wave study shows channel X to be predominant, with an observed barrier of 55.1 k ~ a l / m o l . ~ ' 5. Discussion Having presented our results in detail, we now address the general question of whether semiempirical methods such as MNDO and MNDOC can give useful and reliable information on transition states in chemical reactions. For all systems studied, the qualitative features of the potential surfaces are predicted by MNDO and MNDOC in complete analogy to the ab initio R H F treatments. The same types of minima and transition states are found, the only major exception being the carbene insertion reaction via 23 (see above). When comparing with the best correlated ab initio treatments, MNDO, MNDOC, and ab initio R H F share one particular qualitative deficiency in that they predict significant potential wells for (39) Salem, L. Acc. Chem. Res. 1971, 4, 322. (40) Hepburn, J. W.; Buss, R. J.; Butler, L. J.; Lee, Y. T . J . Phys. Chem. 1983,87, 3638. (41) Saito, K.; Kakumoto, T.; Murakami, I J . Phys. Chem. 1984, 88, 1182.
4430 J . Am. Chem. Soc., Vol. 107, No. 15, 1985
Schroder and Thiel
Table VII. Statistical Evaluation of Transition-State Predictions‘
mean absolute deviation ab initio Nb MNDO MNDOC reference
Prouerty bond length, A 112 activec 70 passivec 42 bond angle, deg 58 dihedral angle, deg 20 activation energy, kcal/mol 24
0.057 0.078 0.018 7.9 11.6 13.6 21.9
0.056 0.073 0.025 6.2 7.9 11.2 8.7
RHF RHF RHF RHF RHF RHF
22 BEST “MNDO and MNDOC vs. ab initio data given in Tables I and IV. bNumber of comparisons. c“Active”bonds are broken or formed in the reaction; “passive” bonds remain formally unchanged.
carbenoid species such as 2, 3, 27, and 30 which disappear at higher theoretical levels. Hence, MNDO and MNDOC seem to be suitable for fast initial scans of potential surfaces to assess their qualitative features, but it has to be kept in mind that some of these characteristics may change at higher levels. With regard to the accuracy of semiempirical transition structures, Table VI1 gives a statistical evaluation of the comparisons with ab initio R H F data in Table I. Apparently, MNDOC reproduces the a b initio R H F transition structures slightly better than MNDO$* the mean absolute deviations being of the order of 0.07 (0.03) A for the bond lengths of “active” (“passive”) bonds, 6’ for bond angles, and 8’ for dihedral angles. Furthermore, in the majority of cases, the MNDOC transition structures are similar to the ab initio R H F ones in the sense that every single deviation in bond lengths and in angles is below 0.1 A and loo, respectively (see Table I). Based on this satisfactory agreement, we may draw two conclusions: First, for large molecules where ab initio calculations might be impossible, we expect semiempirical transition structures to be reliable enough to form the basis of qualitative arguments, e.g., concerning stereochemical problems. Second, for computational studies of medium-size molecules, it seems advantageous to combine semiempirical and ab initio calculations in the following manner: Semiempirical methods can be used efficiently for a fast initial determination of transition structures which can then serve as starting points for automatic ab initio optimizations; this suggestion is supported by the success that we enjoyed with the reverse procedure (see section 3). The M N D O vibrational frequencies for transition states are normally reasonably close to the corresponding ab initio R H F values (see Table VI) so that it might be recommended to use them in RRKM calculations for large molecules.I0 With respect to zero-point vibrational energies, there is generally excellent agreement between M N D O and ab initio R H F (see Table V), the mean absolute deviation being 0.7 kcal/mol (3%) in 39 comparisons; the M N D O values tend to be slightly lower than those from RHF/6-31G* and slightly higher than those from R H F / 3-21G (see Table V). Hence, zero-point vibrational corrections to potential barriers can safely be deduced from semiempirical MNDO-type calculations. Knowing the geometries and the vibrational frequencies of reactants and transitions states, the techniques of statistical thermodynamics may be used to compute activation entropies and kinetic isotope effect^.^^,^^ Based on the satisfactory agreement between semiempirical and ab initio transition-state geometries and frequencies (see above), we expect activation entropies and kinetic isotope effects to be predicted reasonably well by semi(42) For two additional examples, see ref 35 and: Breulet, J.; Schaefer, H.F.,111. J . Am. Chem. Sot. 1984, 106, 1221. (43) Dewar, M . J. S.; Ford, G. P. J . Am. Chem. SOC.1977, 99, 1822. (44) Brown, S . B.; Dewar, M. J. S.; Ford, G. P.; Nelson, D. J.; Rzepa, H. S . J . Am. Chem. SOC.1978, 100, 7832. (45) Reisner, D. E.; Field, R. W.; Kinsey, J. L.; Dai, H. L. J . Chem. Phys. 1984, 80, 5968.
empirical methods. MNDO applications of this kind have indeed been quite successful in several mechanistic s t u d i e ~ . ~ Such J~*~~ applications receive additional support from our present comparisons. Turning to activation energies, the situation appears to be less favorable. Some general trends are obvious from Figure 3 and Table IV: Explicit inclusion of electron correlation normally lowers the calculated activation energies both in semiempirical methods (Le., MNDO > MNDOC) and in ab initio treatments (Le., R H F > BEST). Likewise, a b initio activation energies tend to be somewhat smaller than the corresponding semiempirical ones (Le., M N D O > R H F and MNDOC > BEST in most cases). For a given potential surface, the sequence of activation energies is roughly the same for the different approaches, particularly for MNDOC vs. BEST, although crossings in the correlations do occur (see Figure 3). Table VI1 evaluates the M N D O and MNDOC predictions for activation energies on a statistical basis: Both methods perform similarly with respect to the ab initio R H F results, but MNDOC is far superior when compared to the best correlated ab initio data, the mean absolute deviations being 21.9 kcal/mol for M N D O and 8.7 kcal/mol for MNDOC; the corresponding value for ab initio R H F is 11.2 kcal/mol (see Table IV) . Hence, if we accept the best correlated ab initio results as reliable reference data, MNDOC turns out to be more suitable than MNDO for quantitative estimates of activation energies. This is probably partly due to the explicit inclusion of electron correlation in the MNDOC f ~ r m a l i s m .On ~ the other hand, it should also be pointed out that many reactions studied presently involve carbonmonoxide and carbenes, Le., systems which are known to be problematic for MNDO (not for MNDOC).3,Ss3STherefore, we would generally expect MNDO to approach MNDOC in its predictions more closely when dealing with other systems. In practical applications to large molecules where ab initio calculations might not be feasible, it is often desirable to distinguish between different mechanistic alternatives on the basis of calculated semiempirical activation energies. The preceding results suggest some caution in such an endeavour even though it is often easier to compute relative rather than absolute activation energies (see Figure 3). In our opinion, the semiempirical predictions would seem reliable if the calculated barriers for different pathways differ by large amounts (e.g., larger than the deviations listed in Table VII) or if there are independent error estimates available (e.g., from experience with related reactions). Mechanistic results based on calculated activation energies should preferably be supported by additional evidence derived from transition-state geometries and frequencies (e.g., activation entropies, kinetic isotope effects, stereochemistry, etc.) and by arguments based on the electronic structure of the transition state (e.g., concerning solvent and substituent effects). When applied in such a comprehensive manner, semiempirical calculations are expected to be a valuable tool for studying chemical reactions of large molecules. 6. Conclusion
MNDO and MNDOC usually reproduce the qualitative features of ab initio potential surfaces and transition structures. The calculated semiempirical activation energies are sometimes less accurate than desirable; however, the MNDOC barriers are normally realistic enough to allow correct mechanistic conclusions. The overall agreement between the semiempirical and the ab initio results supports MNDO and MNDOC calculations of transition states for thermal organic reactions, Le., applications in an area not included in the parametrization of these methods. Acknowledgment. This work was supported by the Fonds der Chemischen Industrie. The calculations were carried out by using the Cyber 170-20 of the Hochschulrechenzentrum Wuppertal. Registry No. CzH4,74-85-1; CzH20,463-5 1-4; formaldehyde, 50-00-0; methanol, 67-56-1; propene, 115-07-1; formic acid, 64-18-6; glyoxal, 107-22-2.
